[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close
4 @5 t, r5 t# {& D; m1 |
% n=input('请输入迭代次数：');! K\" l2 r; u& X0 O% c
% qujian=input('请输入初始区间：');( r T# Z8 S0 x8 b2 |0 A! V
n=100;- [8 B1 e0 E+ @5 b' l$ Q/ u+ _
wucha=0.005;
4 c* G8 t5 ~* u1 e2 h- ~
qujian=[0 1];
5 S4 F# C& u0 a4 [\" J3 r
a(1)=qujian(1);/ \6 V4 e6 y c2 x
b(1)=qujian(2); . ^) {0 q# F8 l, L8 `, |2 I
a0=a(1);1 _1 [1 X8 N' t* }0 r0 l+ f' f
b0=b(1);: r3 L3 W! G- W7 d8 |+ z3 [
x=qujian;
2 R\" e% J9 ~0 x1 S7 A
y=exp(x)+10*x-2;
5 ^1 A\" E! [, R* L8 V% j- ?
y1=y(1); %小于0! ~4 w2 w- k+ k9 J! W G3 I: F' v
y2=y(2); %大于0$ T; s0 b4 S! N7 U
for i=1:n %总迭代次数
, o' o9 R+ M) d
c(i)=(a+b)/2; @# u\" |& q$ S w2 [! S
f(i)=exp(c(i))+10*(c(i))-2;! f1 j) ~) e! u9 E3 |
kesai_k(i)=(b-a)/2;
, R6 v' Q4 o- S/ v$ O2 S( u p
if f(i)>05 z3 r; r f2 y: X1 O E+ z
b=c(i);1 h; L* k9 A5 x2 r
b1(i)=c(i);
$ ^; ^: r1 D7 K! K' ~7 G
a1(i)=a;& A- j. r+ ^4 Z* O% w( M
elseif f(i)<0, \+ K+ S5 c- z/ t A5 A
a=c(i);% E1 Y8 C# Q/ j\" }: A
a1(i)=c(i);( z0 T* h; B! R% _; h$ ?
b1(i)=b;
& B2 N+ C: X# C9 G8 F# N$ P4 Q$ j
elseif f(i)==0||kesai_k(i)<=wucha8 M) M) G/ V# S. B
disp('精确值解为：');9 D6 L\" I3 I6 E2 l$ }
disp(c(i));
; d( j: `\" X* U* w4 _& f
break;\" P8 ]( i' A4 s; F
end7 g5 D7 _& r\" }1 q
end/ `2 f( u! l- b- _: {9 k1 \( ~
disp('迭代次数：');
4 V+ c) V) \7 U M1 N5 V$ d
fprintf('%d次\n\n',n);
! o+ E: f/ d: B+ c% K9 C
fprintf('要求误差%f\n\n',wucha);
3 n% F. Y: X6 x9 U
disp('输出矩阵为：');2 `0 L\" F/ L: j
A=[a0 a1]';
6 r+ E1 Y3 M1 }
B=[b0 b1]';4 o- p$ f( T$ Z& Y
format long! r, c. W2 U8 y- P
data_out=[A B c' f' kesai_k']4 [ v& g6 \7 `; b
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：3 V* P) ~+ H) H+ Y# {, h
0.0905 s. `* F' n/ F6 S5 [# s; O
/ g, e$ \6 s- Q1 h% T
迭代次数：3 g/ ^9 t$ p+ x1 M P- |6 W& M
100次
- U! x- N( r$ W' S% d\" q
' v2 J2 I' T8 n$ w' S1 h) a$ }
要求误差0.005000
9 p; x6 t9 N0 @$ {
输出矩阵为：$ ]$ @: _4 X! @- [
) g\" s o; @& |! U' `+ W# u
data_out =
8 g2 q, K7 ^& F7 h. H0 Q
% d9 a1 O; I- ]2 J; H
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000000 F% A0 G6 d7 u
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
) A# \: R8 g m\" Y/ o% u+ B* Q r
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
2 \+ h! k\" Q# u- Q3 s! r( C
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.0625000000000008 s$ i' Q& U* e4 ?: ~
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
6 }; `1 O$ F7 t
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
\" z# o% L8 n' `4 V\" `; {
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000004 P- Z8 e: L, |0 }4 n; G. l+ t; J! P3 T
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
. V- _: M; O; z0 ~1 _0 J( s
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
( Z) A7 u; @: y+ P\" G
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
6 }4 ? _+ U\" D$ O
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000' g$ h7 w: ~/ v0 \8 v5 S
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
! f4 ~8 ~, E5 s
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
8 a; R5 j; |6 E0 R1 q
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
; U; r3 @0 T1 n9 }' s! r) m. v' U6 _
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781253 G/ a\" G: [2 b- W6 o1 Y4 v1 Z/ K
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
0 y5 A4 @ B' v% e
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531- Z9 p- D# Z& @! B0 p
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.0000038146972667 o( U4 \8 {\" U2 N; M9 C6 f+ q
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633: Q- c1 E0 L2 W, q4 G/ |$ @9 H
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.0000009536743166 J3 r6 F! c- t) X
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
3 T0 b/ f3 _; ^: v\" B\" ?+ A
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
$ g7 W2 p( f/ P2 D5 |+ N
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290. ^, m/ j* b2 u- f
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
/ [7 [: b+ s4 k
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322- e5 z\" L8 u\" T+ B& Y: u) s/ F# z
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.0000000149011616 x$ T. f# F) v) U3 i% R$ v
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
& [1 F; t$ ]: k. ?
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
6 v+ I4 Q& V/ c/ h/ M
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645; y+ G+ B2 p; g- \5 v
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
+ X6 N7 b) o\" a, P& y
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656611 [3 ]% P& w* x6 I3 o
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328314 Z O! @+ G. w6 v+ N
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415) M\" \' o& Q1 Y: j/ [% ^0 Z
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208\" Q- @, V7 E1 Q* T& I' n
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104/ r7 }2 t. N C
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552 z: D r, B. T1 `8 \6 R
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276( Z' H/ I7 r, y) O* C. E6 V, E
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638$ {5 b# l' |, j, W6 r2 A( p
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
! y* b+ E; l# t% f/ } c
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009090 t9 X5 T\" P\" y6 k2 G# ~# S. ?
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455* d3 x$ [4 w2 R% B
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227* g |% i0 j- B: @# Y2 L$ [8 \
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
3 b3 T7 u# @0 S6 t
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000573 i2 h0 z6 R' {$ Y4 v: L, H# E
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
\" p* k\" g) T3 A% }
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014! M\" D' |3 \3 j }% u) @# q
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
, E5 y' Q\" h4 e: Z
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000047 `7 t+ {' h0 h8 g( j
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.0000000000000028 Y6 N$ H+ {\" U2 k
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000